Note. This technical report is an extended version of the paper with the same title in the proceedings of Mathematics of Program Construction, 1995, Bad Irrsee, which will be published in the Springer series Lecture Notes in Computer Science.

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Zusammenfassung. Wir stellen die neue Methode FOX vor, die auf die formale Entwicklung sequentieller, objektorientierter Softwaresysteme abzielt. FOX ist eine synergetische Kombination aus der semiformalen Methode Fusion und der formalen Spezifikationssprache Object-Z. Die Methode unterscheidet ausdrücklich Analyse und Entwurf, um die Komplexität und die unterschiedlichen Aufgaben der Softwareentwicklung zu bewältigen. In jeder Entwicklungsphase werden Zustands-und Verhaltensspezifikationen in graphischer oder textueller Form erstellt. Wir geben Beweisverpflichtungen an, um zu gewährleisten, daß die entwickelten Spezifikationen formal konsistent und vollständig sind, und daß das resultierende System zur Ausgangsspezifikation konform ist. Wir illustrieren die Anwendung von F OX an einem einfachen Beispiel, einem Grapheditor.Abstract. We present a new method, called F OX , which aims at the formal development of sequential, object-oriented software systems. F OX is a synergetic combination of the semi-formal Fusion method and the formal specification language Object-Z. To manage complexity and to foster separation of concerns, F OX distinguishes between analysis and design. In each phase structure and behaviour specifications are developed step-by-step. The specifications may be graphical or textual. We give proof obligations to guarantee that the developed models are formally consistent and complete, and that the resulting system conforms to the original specification. By walking through a simple example -a graph editor -we illustrate the application of FOX.

This paper introduces, discusses and proves a transformation rule to convert specifications of set-valued functions defined by set comprehension into functional implementations. The power of the rule is illustrated by several examples, among them a Prolog interpreter. Also, variants of the rule for specifications involving existential quantification and arbitrary choice are presented and illustrated by representative examples.

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